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Irreducible outer automorphisms of a free group


Authors: S. M. Gersten and J. R. Stallings
Journal: Proc. Amer. Math. Soc. 111 (1991), 309-314
MSC: Primary 20E36; Secondary 20E05, 57M05
DOI: https://doi.org/10.1090/S0002-9939-1991-1052571-7
MathSciNet review: 1052571
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Abstract: We give sufficient conditions for all positive powers of an outer automorphism of a finitely generated free group to be irreducible, in the sense of Bestvina and Handel. We prove a conjecture of Stallings (1982), that a PV automorphism in rank $ \geq 3$ has no nontrivial fixed points.


References [Enhancements On Off] (What's this?)

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  • [Ga] F. R. Gantmacher, The theory of matrices, Vol. II, Chelsea, New York, 1959.
  • [Ge] S. M. Gersten, On fixed points of certain automorphisms of free groups, Proc. London Math. Soc. 48 (1984), 72-90. MR 721773 (85k:20075a)
  • [Gr] M. Gromov, Hyperbolic groups, Essays in Group Theory (S. M. Gersten, ed.), MSRI Publication, vol. 8, Springer-Verlag, 1987, pp. 75-263. MR 919829 (89e:20070)
  • [St] J. R. Stallings, Topologically unrealizable automorphisms of free groups, Proc. Amer. Math. Soc. 84 (1982), 21-24. MR 633269 (82m:20030)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1991-1052571-7
Article copyright: © Copyright 1991 American Mathematical Society

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